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Nonlinear Processes in Geophysics An interactive open-access journal of the European Geosciences Union
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Volume 20, issue 6
Nonlin. Processes Geophys., 20, 1023–1030, 2013
https://doi.org/10.5194/npg-20-1023-2013
© Author(s) 2013. This work is distributed under
the Creative Commons Attribution 3.0 License.
Nonlin. Processes Geophys., 20, 1023–1030, 2013
https://doi.org/10.5194/npg-20-1023-2013
© Author(s) 2013. This work is distributed under
the Creative Commons Attribution 3.0 License.

Research article 25 Nov 2013

Research article | 25 Nov 2013

Modelling and simulation of waves in three-layer porous media

S. R. Pudjaprasetya S. R. Pudjaprasetya
  • Mathematics Department, Institut Teknologi Bandung, Jalan Ganesha 10, Bandung, 40132, Indonesia

Abstract. The propagation of gravity waves in an emerged three-layer porous medium is considered in this paper. Based on the assumption that the flow can be described by Darcy's Law, an asymptotic theory is developed for small-amplitude long waves. This leads to a weakly nonlinear Boussinesq-type diffusion equation for the wave height, with coefficients dependent on the conductivities and depths of each layer. In the limit of equal conductivities of all layers, the equation reduces to the single-layer result recorded in the literature. The model equations are numerically integrated in the case of an incident monochromatic wave hitting the layers. The results exhibit dissipation and also a downstream net height rise at infinity. Wave transmission coefficient in three-layer porous media with conductivity of mangrove is discussed. Numerically, propagation of an initial solitary wave through a porous medium shows the emergence of wave reflection and transmission that both evolve as permanent waves. Additionally we examine the impact of a solitary gravity wave on a porous medium breakwater.

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